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Appendix: J.

fluid pressure is admitted. We therefore require an inordinate
thickness.

But if we cause the core, during casting, to lose its heat more
rapidly than does the exterior, by circulating cold water through
a central pipe, the inside will cool first, and a tension will be
caused on the outside while a compressive hoop stress is felt on
the inner rings.

Building now the (fluid7 hoop stress on the new inclined line,
we obtain the dotted curve shewn in Fig. 752 The hoop stress
is generally more equalised, and the internal hoop stress (or
maximum) is decreased by the value of the initial compression.
Again, therefore, we have been enabled to decrease the stress,
and consequently the necessary thickness^ by the artifice of initial
stressing, caused by casting with a cold-water core.

Building-up from separate tubes, or by tube and wire, must,
however, be looked on as the very best methods, where, in fact,
an almost certain desired result maybe obtained. (See App. JL,
p. 841.)

P. 4.07. Pitch of Riveting.—It should be distinctly under-
stood that the formula, pitch = 1^09 -t-^i is only true if we use
steel both for rivets and plates, and that we do not adopt plates
above an in,ch in thickness. All other cases must be referred to
the general formula on p. 407. The diameter of the rivet for a
particular plate has, up to the present time, been fixed by practical
considerations of punching. It is open to question, now that
boilers are drilled, whether some alteration may not with advantage
be made, tending to increase the diameter of the rivet for thin
plates. (See Appendix: ///,/. 921.)

JPj>. 442-6. Position of Supports for Least Bending
Moment.—Let the beam A B, Fig. 753, be loaded uniformly,
and let it be required to find the position of the two supports
when the least bending moment shall act upon the beam. This
will occur when the maximum stress caused by the load between
c and D is equal to that caused by the loads at A. c and
D B. Thus, if we considered only the loads at A c and D B, a
uniform bending moment is caused by them between c and D,
and this moment has to be completely balanced by that at the```